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Genus-two trisections are standard

Jeffrey Meier and Alexander Zupan

Geometry & Topology 21 (2017) 1583–1630

We show that the only closed 4–manifolds admitting genus-two trisections are S2 × S2 and connected sums of S1 × S3, 2 and ¯2 with two summands. Moreover, each of these manifolds admits a unique genus-two trisection up to diffeomorphism. The proof relies heavily on the combinatorics of genus-two Heegaard diagrams of S3. As a corollary, we classify tunnel number one links with an integral cosmetic Dehn surgery.

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trisections, Heegaard splittings, waves
Mathematical Subject Classification 2010
Primary: 57N12, 57R65
Secondary: 57M25
Received: 1 December 2014
Revised: 21 February 2016
Accepted: 25 March 2016
Published: 10 May 2017
Proposed: Colin Rourke
Seconded: David Gabai, Ronald Stern
Jeffrey Meier
Department of Mathematics
Indiana University
Rawles Hall 425
831 East 3rd Street
Bloomington, IN 47405
United States
Alexander Zupan
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin, TX 78712
United States